TOKYO, Sept 15 (Reuters) - Japan's Nikkei share average rose to its highest in more than two months on Friday, tracking overnight gains in Wall Street, with technology stocks leading the way after the strong market debut of SoftBank Group's Arm Holdings.

The Nikkei was up 1.34% to 33,613.52 by the midday break, its highest since July 3, and is set to rise 3% for the week.

The broader Topix rose 1.25% to 2,435.62 and is on course to post a 3.25% weekly gain.

"First of all, the market rose because Wall Street was strong," said Shoichi Arisawa, general manager of the investment research department at IwaiCosmo Securities.

"And the strong debut of Arm has raised investor sentiment and prompted them to buy chip-related shares."

U.S. stocks ended sharply higher overnight as robust economic data failed to budge expectations that the Federal Reserve will leave its key interest rate unchanged next week.

Adding to positive sentiment, SoftBank Group's Arm was valued at nearly $60 billion in a strong Nasdaq debut overnight, with the chip designer's shares soaring nearly 25% in their first day of trading.

Shares in SoftBank Group rose as much as 5% earlier in the session but trimmed most of their gains to end the morning session up 1.72%.

In Japan, chip-making equipment maker Tokyo Electron rose 3.11% to give the biggest boost to the Nikkei. Chip-testing making equipment maker Advantest gave up early losses to edge up 0.15%.

Sensor systems maker TDK rose 2.26% and air conditioner maker Daikin Industries gained 2.26%.

Refiners jumped 4% to become the top performer among the Tokyo Stock Exchanges' 33 industry sub-indexes. Energy explorers rose 2.97% and the utility sector gained 2.74%.

Retailers and airlines were the only sectors that fell. (Reporting by Junko Fujita; Editing by Sonia Cheema)